Nor will they ever ask for your password.
From Paypal: "PayPal and its representatives will NEVER ask you to reveal your password. There are NO EXCEPTIONS to this policy. If anyone claiming to work for PayPal asks for your password under any circumstances, by email or by phone, please refuse and immediately contact us via webform at https://www.paypal.com/wf/f=sa_pass".
Here is the "scam" letter I received that had a form on the bottom to fill out with account password and credit card number.
Dear PayPal Customer ,
This e-mail is the notification of recent innovations taken by PayPal to detect inactive customers and non-functioning mailboxes.
The inactive customers are subject to restriction and removal in the next 3 months.
Please confirm your email address and credit card information by logging in to your PayPal account using the form below:
The Internet is obviously a terrific place to find sought after items and collectibles, with Paypal providing a great way to help pay for purchases. But Be Wise and BeWare before giving confidential information out to anyone. Make sure you are on a secure site and never respond or give personal information in an email.
If you feel an email might be legitimate log onto to the Paypal site separately, do not use any link provided in an email, then check out your account on the secure site.